Nuprl Lemma : EquatePairs_wf
∀[x,y,n,m:Base].
(EquatePairs(x;n;y;m) ∈ Type) supposing ((¬(n = m ∈ Base)) and (¬(x = m ∈ Base)) and (¬(y = n ∈ Base)))
Proof
Definitions occuring in Statement :
EquatePairs: EquatePairs(x;n;y;m),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
base: Base,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
EquatePairs: EquatePairs(x;n;y;m),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
and: P ∧ Q,
or: P ∨ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
not: ¬A,
false: False
Lemmas referenced :
pertype_wf,
not_wf,
equal_wf,
base_wf,
or_wf,
equal-wf-base,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
independent_isectElimination,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
isect_memberEquality,
because_Cache,
lambdaEquality,
productEquality,
lambdaFormation,
unionElimination,
inlFormation,
productElimination,
inrFormation,
independent_pairFormation,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[x,y,n,m:Base]. (EquatePairs(x;n;y;m) \mmember{} Type) supposing ((\mneg{}(n = m)) and (\mneg{}(x = m)) and (\mneg{}(y = n)))
Date html generated:
2016_05_15-PM-03_15_42
Last ObjectModification:
2015_12_27-PM-01_05_05
Theory : general
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